Three Dimensional Geometry
Find the equation of the plane which contains two parallel lines given by 1x−3=−4y+2=5z and 1x−4=−4y−3=5z−2.
Find the equation of the plane passing through the point (−1,3,2) and perpendicular to each of the planes x+2y+3z=5and3x+3y+z=0.
Shortest distance between the lines 1x−1=1y−1=1z−1and1x−2=1y−3=1z−4 is equal to a. 14 b. 7 c. 2 d. none of these
The equation of the plane through the intersection of the planes x+2y+3z−4=0and4x+3y+2z+1=0 and passing through the origin is (a) 17x+14y+11z=0 (b) 7x+4y+z=0 (c) x+14+11z=0 (d) 17x+y+z=0
Find the equations of the bisectors of the angles between the planes 2x−y+2z+3=0and3x−2y+6z+8=0 and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.
If A(3,2,−4),B(5,4,−6)andC(9,8,−10) are three collinear points, then find the ratio in which point C divides AB˙